An engine stop control is known which automatically temporarily stops an engine when a predetermined engine stop condition holds and automatically restarts the engine when a restart condition holds. For example, an idle stop control and a coast stop control are known as the engine stop control.
The idle stop control stops an engine when a vehicle stops and an idle stop condition holds and restarts the engine when a brake is off and the idle stop condition no longer holds.
The coast stop control stops an engine when an accelerator is off and a brake is on to set a coast state and a vehicle speed is equal to or below a predetermined vehicle speed while a vehicle is running, and restarts the engine when the accelerator is on or the brake is off and the coast stop condition no longer holds.
When the engine is stopped by the above engine stop control, a mechanical oil pump driven by the engine also simultaneously stops. Accordingly, it is disclosed in JP2007-247910A that an electrical oil pump which is operated by power stored in a battery is provided separately from a mechanical oil pump and a working pressure of a transmission is ensured by driving the electrical oil pump during an engine stop control.